"Gebrauchsmusik" Hindemith called it, a term dustily rendered in the usual translations as "Music for Use" or "Practical Music." Gebrauchsmusik, was, however, far more than simply a compositional gimmick or a mere marketing strategy – it was a basic tenet of Paul Hindemith's artistic philosophy.

Throughout his life, Hindemith was a practical musician: a performer, teacher, administrator and conductor as well as a composer. As a boy, he learned to play piano, violin, viola and drums, and he earned his living as a young man performing in dance halls, theaters and cafés. This activity was not simply a dilettantish sideline for him, however – he was a performer of virtuoso stature, the concertmaster of the Frankfurt Opera Orchestra for eight years, violist and founding member of the famed Amar Quartet, and soloist in the 1929 premiere of William Walton's Viola Concerto. To increase his knowledge of the inner workings of the orchestra, he undertook a study of each of the instruments, and eventually became proficient on fourteen of them. His work as a teacher of composition at the Berlin Hochschule für Musik beginning in 1927 and, after he came to the United States in 1940, at Yale University emphasized the practical side of his profession: he wrote a children's opera (Wir bauen eine Stadt – "We're Building a City"), a choral piece with audience participation, sonatas for each of the orchestral instruments, and compositions for pianola, brass band, radio, theater and films; he once taught a course in film music that included giving the students assignments of writing scores for old silent movies. The title of his treatise is indicative of his pragmatic approach to creative activity: The Craft of Musical Composition.

Though Hindemith originally intended his Gebrauchsmusik to serve as relatively easy material in a modern idiom for the performing musical amateur (the Educational Works for Violin Ensembles in First Position, the children's opera Wir bauen eine Stadt and the participatory Lehrstück, or "Training Piece," are representative examples), he also wrote many scores for professional performers that are included in this genre, notably for those instruments he felt had been neglected by earlier composers. Among the most important of these latter pieces are the 25 sonatas he composed after 1935: one or more for each of the orchestral instruments, including harp, a quartet of horns, trombone, English horn and bass tuba. There is even one for E-flat alto horn that is prefaced by a poem spoken from the stage.

The sonatas for the orchestra's two foundational instruments – double bass and tuba – were the last such works that Hindemith composed. The Double Bass Sonata was written quickly in August 1949 (the Tuba Sonata followed in 1955), while he and his wife, Gertrud, were making a long car trip from New Haven across the upper Midwest to Colorado Springs, where he lectured and conducted for a week, then through New Mexico, Texas and along a southern route home. Hindemith was back in New England in time to take up his appointment as Charles Eliot Norton Lecturer at Harvard in October. The opening movement is in a compact sonata form, with a march-like main theme given by the bass and an angular second subject presented by the piano above a pizzicato supporting line. After a brief, legato passage high in the bass' compass, the second theme and then the first return, with a variant of the second subject and a coda built around the main theme filling out the remainder of the movement. The compact Scherzo is a three-section affair: a nimble principal theme for the bass; quicker passagework for the piano with a long-note commentary from the bass; and a repeating-phrase strain with piano and bass in close dialogue. An echo of the opening serves as a postlude. The third movement is a set of six variations on the theme presented at the outset that divides the musical responsibilities almost equally between the participants. A Recitativo passage, featuring piano and then bass, provides a bridge to the finale, a short, graceful Lied ("Song") exploiting the bass' burnished baritone register.